文章基本信息

标题：Association arrays in assessing forms of dependencies between bivariate random variables
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作者：Samuel Karlin
期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：1983
卷号：80
期号：2
页码：647-651
DOI：10.1073/pnas.80.2.647
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：The bivariate distribution of pairs of random variables (X,Y) is said to be associated with respect to the classes of functions [unk] and [unk] if the product-moment correlation r[{Phi}(X),{Psi}(Y)] [≥] 0 for all {Phi} {euro} [unk] and {Psi} {euro} [unk]. In the case in which both [unk] = [unk] = [unk]* consist of all increasing functions, then the bivariate distribution of (X,Y) is said to be positive quadrant dependent. To apply the concept to data, I examine the correlations for classes of extremal functions that span by positive combinations the totality of functions {Phi} {euro} [unk] and {Psi} {euro} [unk] to investigate whether the pair of random variables (X,Y) are associated with respect to [unk] and [unk] and to assess the relative degree (or strength) of association when comparing two sets of random variables (X,Y) and (Z,W).
关键词：bivariate strong association ; positive quadrant dependence ; representative association matrix ; correlation versus association